Subdiffusion equation with Caputo fractional derivative with respect to another function in modelling diffusion in a complex system consisting of matrix and channels

TL;DR

This paper introduces a generalized subdiffusion equation with a Caputo fractional derivative relative to another function, effectively modeling ultraslow antibiotic diffusion in complex matrix-channel systems, with broader applicability in science.

Contribution

It presents a novel fractional diffusion model with a variable time scale, extending traditional equations to better describe complex, evolving diffusion processes.

Findings

Ultraslow diffusion of colistin observed in the system.

The generalized equation captures time-evolving subdiffusion parameters.

Model applicable to various complex diffusion systems.

Abstract

Diffusion equation with a fractional Caputo time derivative with respect to another function $g$, which defines new time scale of the process, is applied to describe anomalous diffusion of antibiotic (colistin) in a system consisting of packed gel (alginate) beads immersed in water and impregnated with the antibiotic. We show that ultraslow diffusion of colistin in the system occurs. The equation, which is more general than the "ordinary" fractional subdiffusion equation, can be widely used in various fields of science to model diffusion in a matrix with channels system when subdiffusion parameters and even a type of diffusion evolves over time.